Exercise 1.  State where the following mappings are conformal.  

1. (a)   .  

Solution 1 (a).

See text and/or instructor's solution manual.

Answer.     is conformal for all  z.  

Solution.   Calculate and determine where  .  

                    

It is known that    for all  .

Therefore,   is conformal for all  z.  

We are done.   

Aside.  We can let Mathematica double check our work.

We are really done.   

Aside.  We can let Mathematica illustrate our work.

                    A small portion of the mapping  .  

                    Another small portion of the mapping  .  

Remark.  In Section 10.3 and Section 10.4 we will study some composite mappings involving  .

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell